Method and system for correcting a mask pattern design

ABSTRACT

A pattern verification method comprising preparing a desired pattern and a mask pattern forming the desired pattern on a substrate, defining at least one evaluation point on an edge of the desired pattern, defining at least one process parameter to compute the transferred/formed pattern, defining a reference value and a variable range for each of the process parameters, computing a positional displacement for each first points corresponding to the evaluation point, first points computed using correction mask pattern and a plurality of combinations of parameter values obtained by varying the process parameters within the variable range or within the respective variable ranges, the positional displacement being displacement between first point and the evaluation point, computing a statistics of the positional displacements for each of the evaluation points, and outputting information modifying the mask pattern according to the statistics.

CROSS-REFERENCE TO RELATED APPLICATIONS

This application is based upon and claims the benefit of priority fromprior Japanese Patent Application No. 2003-421349, filed Dec. 18, 2003,the entire contents of which are incorporated herein by reference.

BACKGROUND OF THE INVENTION

1. Field of the Invention

This invention relates to a pattern verification method, a patternverification system, a mask manufacturing method and a semiconductordevice manufacturing method to be used for manufacturing a semiconductordevice, a liquid crystal display element or the like.

2. Description of the Related Art

The progress of semiconductor manufacturing technologies in recent yearsis very remarkable. Semiconductor devices with a minimal processing sizeof 0.18 μm are currently being manufactured. Such micronization has beenmade feasible by the advancement of micro pattern forming technologiesincluding mask process technologies, photolithography technologies andetching technologies. In the era when large pattern sizes are common,the surface profile of the LSI pattern to be formed is drawn on a waferas mask pattern and a mask pattern exactly the same as the first maskpattern is formed and transferred onto the wafer by means of aprojection optical system so that a pattern substantially identical withthe first mask pattern is formed on the wafer by etching the underlyinglayer. However, in the course of micronization of mask patterns, it hasbeen increasingly difficult to form a pattern exactly the same as thefirst pattern in the pattern forming process to give rise to a problemthat the final dimensions of the finished product to not exactly agreewith those of the mask pattern.

Particularly, in the case of lithography and etching process that isessential to micro-processing, the dimensional precision of a pattern tobe formed is significantly influenced by the layout environment of thepatterns other than the pattern to be formed that are arranged aroundthe pattern. Thus, the optical proximity correction (OPC) technique andthe process proximity correction (PPC) technique (to be referred to asPPC technique hereinafter) of adding an auxiliary pattern to a maskpattern in advance have been reported with the aim of reducing theinfluence and forming a desired pattern with the intended dimensionsafter the micro-processing operation.

As the optical proximity correction (OPC) technique and the processproximity correction (PPC) technique have become more sophisticated thanever, it is currently not easy to predict the profile of the pattern tobe finished on a wafer because of the large difference between thepattern designed by a designer and the mask pattern that is actuallyused at the time of exposure to light and hence it is necessary toverify the finished product by means of a lithography simulator. D. M.Newmark et al., “Large Area Optical Proximity Correction Using PatternBased Correction”, SPIE Vol. 2322 (1994) 374, proposes a verificationtool for comparing the edges of a desired pattern to be formed on awafer and those of the pattern transferred by using the layout after OPCand checking if the difference is found within a predetermined allowablerange or not.

Japanese Patent Application Laid-Open No. 9-319067 proposes a techniquefor highly precisely predicting the positional displacement between theedges of a desired pattern and those of the corresponding transferredpattern by preparing physical models for proximity correction andverification. According to this proposal, a means for dissolving theproblem of consuming a vast amount of time for verification at the fullchip level of the device is also provided. More specifically, the abovecited patent document proposes a verification technique realized bycombining a rule-based correction technique of conducting correctionsaccording to predetermined correction rules and a simulation-basedcorrection technique of using a simulator for preparing models ofphenomena that appear as a result of the exposure/development process.

To date, it has been possible to output the results of a transfersimulation realized by repeating the operation of optical proximitycorrection (OPC) and using the layout of the finished mask and that ofthe mask obtained as a result of the repeated OPC operation. However,the obtained information does not contain information that tells thedesigner about how to draw the layout.

Additionally, with the known verification processes using a lithographysimulator, it is necessary to compute the light intensity at manyevaluation points to make them very time-consuming ones. Therefore,there is a strong demand for a verification process that can improve theturnaround time (TAT) of the flow of the verification process.

Meanwhile, patterns on wafers are accompanied by problems that canroughly be classified into two types. One is that the obtained patternshows discrepancies from the desired pattern regardless of theconditions under which the transfer operation is conducted and the otheris that the obtained pattern does not give rise to any problem under“ideal” conditions but shows discrepancies once the process conditionschange.

However, it is not possible to discriminate the above two types ofproblems for the produced pattern because what is output by any of theknown techniques is the data obtained by comparing the produced patternwith the desired pattern, or the “ideal” pattern.

As discussed above, to date, while it has been possible to output theresults of verification of the desired pattern and the mask pattern, ithas not been possible to provide the designer with a guideline when themask pattern requires to be modified. Additionally, it is desired toimprove the TAT of the flow or the verification process. Stilladditionally, while it has been possible to compare the desired patternand the mask pattern, it has not been possible to tell if the problem,if any, of a pattern is attributable to the desired pattern or to theprocess conditions.

BRIEF SUMMARY OF THE INVENTION

In an aspect of the present invention, there is provided a patternverification method comprising: preparing a desired pattern and a maskpattern for forming the desired pattern on a substrate; defining atleast one evaluation point on an edge of the desired pattern; definingat least one process parameter for computing the transferred/formedpattern; defining a reference value and a variable range for each of theprocess parameters; computing a positional displacement for each firstpoints corresponding to the evaluation point, first points computedusing correction mask pattern and a plurality of combinations ofparameter values obtained by varying the process parameters within thevariable range or within the respective variable ranges, the positionaldisplacement being displacement between first point and the evaluationpoint; computing a statistics of the positional displacements for eachof the evaluation points; and outputting information for modifying themask pattern according to the statistics.

In another aspect of the present invention, there is provided a patternverification method comprising: preparing a desired pattern and a maskpattern for forming a first formed pattern corresponding to the desiredpattern on a substrate; generating edges by dividing the edge of themask pattern by a predetermined length; defining a correction point oneach of the edges generated by dividing the edge of the desired pattern;computing a correction quantity in consideration of the proximity effectfor each of the correction points; forming a correction mask pattern bymoving the generated edges according to the computed correctionquantities; defining at least one evaluation point on the edge of thecorrection mask pattern; defining at least one process parameter forforming a pattern which being resist pattern formed on the substrate byusing the correction mask pattern or being pattern formed in thesubstrate by using the resist patterns as a mask; defining a referencevalue and a variable range for each of the process parameters forforming the second transferred/formed pattern; computing firsttransferred/formed patterns which being resist patterns formed on thesubstrate or being patterns formed in the substrate by using the resistpatterns as a mask, the first transferred/formed patterns being computedusing correction mask pattern and a plurality of combinations ofparameter values obtained by varying the process parameters within thevariable range or within the respective variable ranges; computing apositional displacement of the corresponding edge from the evaluationpoint of the edge of the pattern transferred/formed on the substratefrom the correction mask pattern; computing a statistic of thepositional displacements for the evaluation points; and outputtinginformation for modifying the mask pattern according to the statistic.

BRIEF DESCRIPTION OF THE SEVERAL VIEWS OF THE DRAWING

FIG. 1 is a flow chart summarily illustrating the sequence of a firstembodiment of pattern verification method according to the invention;

FIGS. 2A through 2D are illustrations of the first embodiment of patternverification method according to the invention;

FIG. 3 is a flow chart of the sequence of the operation of determiningthe positional displacement of the edges;

FIG. 4 is a graph schematically illustrating the light intensity on thesubstrate as obtained from a mask pattern;

FIG. 5 is a schematic illustration of a recommended pattern to be usedfor forming a desired pattern;

FIG. 6 is a graph illustrating the frequency distribution of positionaldisplacements;

FIG. 7 is a graph illustrating the frequency distribution of positionaldisplacements;

FIG. 8 is a flow chart summarily illustrating the sequence of a secondembodiment of pattern verification method according to the invention;

FIGS. 9A through 9E are illustrations of the second embodiment ofpattern verification method according to the invention;

FIG. 10 is a schematic illustration of the results of an operation ofgenerating patterns near an edge of a desired pattern by varying theprocess parameter within a predetermined range;

FIG. 11 is a schematic illustration of a recommended pattern to be usedfor forming a desired pattern;

FIG. 12 is a schematic illustration of a method of displaying a markerthat indicates the positional displacement of the edges when a singleprocess parameter is used;

FIG. 13 is a schematic illustration of a method of displaying markersthat respectively indicate the positional displacements of the edgeswhen more than one process parameters are used;

FIG. 14 is a schematic illustration of a concentration method used forcorrection;

FIG. 15 is a schematic illustration of another concentration method usedfor correction;

FIGS. 16A and 16B are schematic illustrations of a pattern that can beused for a third embodiment of the invention;

FIG. 17 is a graph illustrating the positional displacements under thebest focus/best dose conditions;

FIG. 18 is a graph illustrating the differences between the conventionalmethod and the slope method and the differences between the splinemethod and the conventional method under the best focus/best doseconditions;

FIG. 19 is a graph illustrating the positional displacements under thedefocus/best dose conditions;

FIG. 20 is a graph illustrating the differences between the conventionalmethod and the slope method and the differences between the splinemethod and the conventional method under the best focus/best doseconditions;

FIG. 21 is a graph illustrating the positional displacements under thebest focus/best dose conditions;

FIG. 22 is another graph illustrating the differences between theconventional method and the slope method and the differences between thespline method and the conventional method under the best focus/best doseconditions;

FIG. 23 is a graph illustrating the positional displacements under thedefocus/best dose conditions;

FIG. 24 is a graph illustrating the differences between the conventionalmethod and the slope method and the differences between the splinemethod and the conventional method under the defocus/best doseconditions;

FIG. 25 is a flow chart summarily illustrating the sequence of a fourthembodiment of pattern verification method according to the invention;

FIG. 26 is a graph illustrating the ED-tree to be referred to whendescribing the fourth embodiment of pattern verification method;

FIG. 27 is a graph illustrating the results of an operation ofdetermining the margin of the same layout by means of the conventionalmethod and also by means of this embodiment of method;

FIG. 28 is a flow chart summarily illustrating the sequence of a seventhembodiment of pattern verification method according to the invention;

FIGS. 29A and 29B are schematic illustrations of a desired pattern and acorresponding mask pattern;

FIGS. 30A and 30B are schematic illustrations of a pattern and a desiredpattern and error mark obtained by simulation; and

FIG. 31 is a schematic illustration of an eighth embodiment of thepresent invention, which is a pattern verification system.

DETAILED DESCRIPTION OF THE INVENTION

Now, embodiments of the present invention will be described in greaterdetail with reference to the accompanying drawings.

1st Embodiment

FIG. 1 is a flow chart summarily illustrating the sequence of the firstembodiment of pattern verification method according to the invention.FIGS. 2A through 2D are illustrations of the first embodiment of patternverification method according to the invention.

Firstly, draft circuit pattern data that are necessary for securing thedevice characteristics when designing an LSI or the like are prepared.Data for a mask pattern that is an enlarged draft circuit pattern arealso prepared by taking the scale reduction ratio of the projectionoptical system of an aligner (Step ST11). FIG. 2A illustrates a desiredpattern 10 that is contained in a draft circuit layout. A total of nevaluation points Pi (i=1 through n) are defined along the edges of thedesired pattern 10 that is contained in the design data (Step ST12). Theevaluation points are generated at respective positions whosecoordinates are specified in advance and an evaluation point is arrangedwithout fail at a point separated from each corner by 100 μm.

Reference values (design values) are defined for the process parametersthat can give rise to positional displacements of pattern edges (StepST31). The process parameters may include the film thickness of theresist film, the numerical aperture NA, the dose and the parameters forexposure including the defocusing value as well as post-exposureparameters such as the PEB temperature and the development time.

Then, a variable range relative to the reference value is defined foreach process parameter (Step ST32). In this embodiment, the variablerange of the dose is defined in terms of under dose˜the best dose ˜overdose. The variable range of the focus position is defined in terms ofthe best focus˜defocus. The process parameters other than the dose andthe focus position are made invariable from the defined values.

The following processing operation is conducted for all the definedevaluation points (Step ST13 through ST16). The value of each processparameter is modified within the defined variable range thereof in StepST12 and the positional displacement of the evaluation point Pi (i=1) isdetermined for a plurality of combinations of parameter values (StepST14). In this embodiment, three combinations including (the bestdose/the best focus), (over dose/defocus) and (under dose/defocus) areused to compute the positional displacement of the edges. However, it ispossible to compute for all possible combinations of doses and focusessimultaneously without any additional load. At the same time, it is alsopossible to compute the positional displacements that can be producedjust like the defined dose, the defined focus, the process parameters,the numerical aperture of the aligner, the coherence factor, the centershielding ratio and/or the aberration change. It is also possible to useall or part of the parameters of the items that can participate inpositional displacement and hence the parameters that are used in thisembodiment are not limited to those listed above.

Now, the method of determining the positional displacement will bedescribed by referring to FIG. 3. FIG. 3 is a flow chart of the sequenceof the operation of determining the positional displacement of theedges.

Firstly, the reference light intensity (I_(th)) is defined to form thedesired pattern 10 on a wafer in order to meet the requirements imposedby the subsequent photo-etching process and other processes (Step ST31).

Subsequently, the light intensity I(t₁) at the evaluation point P_(i)with the positional coordinate t₁ on the desired pattern 1 is computedby using the Hopkins formula (formula (1)) (Step ST32);

$\begin{matrix}{{I(t)} = {\int{\int_{- \infty}^{\infty}{{{TCC}\left( {\omega,\omega^{\prime}} \right)} \times {M(\omega)} \times {{M\left( \omega^{\prime} \right)}\ }^{*} \times \exp \left\{ {{\left( {\omega - \omega^{\prime}} \right)}t} \right\} {\omega}{\omega^{\prime}}}}}} & (1)\end{matrix}$

where TCC (ω, ω):transmission cross coefficient, ω, ω′:spatialfrequency.I(t):function for expressing the light intensity at positionalcoordinate t;M(ω):Fourier transform of mask complex transmission distribution on thefrequency plane,M(ω′):complex conjugate of Fourier transform of mask complextransmission distribution on the frequency plane andi:imaginary unit.

To compute the light intensity I(t₁) by using the Hopkins formula, it isnecessary to carry out the following computations in advance.

(1) preparation of mask pattern data defining the complex amplitudetransmission distribution from the mask pattern and computation of themutual transmission coefficient TCC(ω, ω′)(2) Fourier transformation of the complex amplitude transmissiondistribution of the mask pattern to obtain M(ω) and M*(ω)(3) computation of the product of multiplication of the mutualtransmission coefficient TCC(ω, ω′), the Fourier transform M(ω) andM*(ω′) (TCC(ω, ω′)×M(ω)×M*(ω′)).(4) Inverse Fourier transformation of the mutual transmissioncoefficient TCC(ω, ω′)×M(ω)×M*(ω′).(5) Integration of the product of multiplication of {TCC(ω,ω′)×M(ω)×M*(ω′)} and exp{i(ω−ω′)t} for ω, ω′.

Then, the first derivative I′(t₁) of the light intensity I(t₁) at theevaluation point P_(i) with the coordinate t₁ is computed by usingformula (2) below (Step ST33).

$\begin{matrix}{{I^{\prime}(t)} = {\int{\int_{- \infty}^{\infty}{{{TCC}\left( {\omega,\omega^{\prime}} \right)} \times {M(\omega)} \times {{M\left( \omega^{\prime} \right)}\ }^{*} \times {\left( {\omega - \omega^{\prime}} \right)} \times \exp \left\{ {{\left( {\omega - \omega^{\prime}} \right)}t} \right\} {\omega}{\omega^{\prime}}}}}} & (2)\end{matrix}$

In the computation using the above formula (2), the part ofexp(i(ω−ω′)t) that requires a large computational load is determined byreferring to the result of computation obtained when determining thelight intensity I(t₁) in Step ST32.

Then, the CD displacement X is determined by using formula (3) below,the light intensity I(t₁), the first derivative I′(t₁) of the lightintensity and the reference light intensity Ith (Step ST34).

$\begin{matrix}{X = \frac{I_{th} - {I\left( t_{1} \right)}}{I^{\prime}\left( t_{1} \right)}} & (3)\end{matrix}$

Now, the reason why the positional displacement X can be determined fromthe formula (3) above will be described with reference to FIG. 4. FIG. 4is a graph schematically illustrating the light intensity on thesubstrate as obtained from a mask pattern.

The first derivative I′(t₁) indicates the slope at position t₁ of thefunction I(t) expressing the light intensity. Assume that the linearfunction that passes through position (t₁, I(t₁)) and shows an slope t₂is expressed by I′ (t₁)×t+c (where c is a constant). The positionalcoordinate t′₁ of the slope of the linear function f(t) and I_(th) is(I_(th)−c)/I′(t₁) from the linear function. t₁=(I(t₁)−c)/I′(t₁). Sincethe positional displacement X is t₂−t₁, it can be determined from theformula (3) above.

Similarly, when the light intensity distribution at and near anarbitrarily selected coordinate t on the desired pattern is approximatedby the second derivative I″ (t) of the light intensity distribution, therelationship between the reference light intensity I_(th) and the CDdisplacement X is expressed by formula (4) below.

$\begin{matrix}{I_{th} = {{\frac{1}{2}{I^{''}(t)}X^{2}} + {{I^{\prime}(t)}X} + {I(t)}}} & (4)\end{matrix}$

Thus, the CD displacement X is given by solving quadratic equation (5)below.

$\begin{matrix}{X = \frac{{- {I^{\prime}(t)}} \pm \sqrt{{{I^{\prime}(t)} \times {I^{\prime}(t)}} - {2 \times {I^{''}(t)} \times \left( {I_{th} - I} \right)}}}{I^{''}(t)}} & (5)\end{matrix}$

At and near each corner, the positional displacement in each of the tworectangularly intersecting directions is determined.

Then, the average value and the standard deviation of the positionaldisplacements of all the evaluation points P_(i) (i=1 through n) aredetermined (Step ST17). Then, it is determined if the standard deviationis found within the predefined variable range for positionaldisplacement or not (Step ST18).

If the standard deviation is found to be out of the predefined variablerange for positional displacement, the desired pattern has to bemodified (Step ST19). The largest positional displacement of the edge isextracted for each evaluation point and a pattern 11 is prepared byconnecting the extracted positional displacements (FIG. 2C). In theinstance of FIG. 2C, the desired pattern 10 is dimensionally reducedaccording to the scale reduction ratio of the aligner so that thedesired pattern 10 and the pattern 11 are drawn on the same scale. Then,another pattern 12 is generated with edges shifted from those of thedesired pattern by the largest positional displacements (FIG. 2D) and apattern is generated with edges shifted in opposite directions by theamounts obtained by dividing the extracted largest positionaldisplacements by the MEF (mask error factor, or the ratio of thedimensional change relative to the variance of the mask) so as to beused as recommended draft layout.

When the standard deviations is found to be within the predefinedvariable range for positional displacement, it is determined if theaverage of the positional displacements is found within a predefinedrange for average or not (Step ST20). If the average of the positionaldisplacements is found to be out of the predefined variable range foraverage, the mask pattern has to be modified (Step ST21).

FIG. 5 shows a result of a recommended pattern obtained by using thetechnique of this embodiment. In FIG. 5, reference symbol 13 denotes arecommended pattern (mask pattern) to be used for forming a desiredpattern on a wafer. It is possible to form a desired pattern on a waferby drawing a layout, shifting the edges according to the obtainedresults.

In other words, it is possible to form a desired pattern on a wafer bymodifying the draft layout according to the output layout or provide adesign guideline.

If a plurality of evaluation points are used on the desired pattern inStep ST33, the same X coordinate and the same Y coordinate can be sharedby more than one evaluation points because evaluation points arearranged linearly. Thus, it is only necessary to carry out thecomputation of inverse Fourier transformation that involves a heavycomputational load for acquiring an optical image only once for anevaluation point because the result of the computation can be referredto for all the remaining evaluation points. In other words, thecomputational load of this embodiment does not rise significantly if thenumber of evaluation points is increased to raise the level of accuracyof evaluation.

As a result of an experiment using a conventional technique and thetechnique of this embodiment and common data for the same process, itwas found that the conventional technique consumed 420 hours, whereasthe technique of this embodiment consumed only 36 hours.

In this embodiment, the dispersion and the average value of positionaldisplacements are used to determine if the mask pattern needs to bemodified or not. However, it should be noted that the dispersion ofpositional displacements can be asymmetric depending on the parameterthat is made variable. FIGS. 6 and 7 are illustrations that support theabove description. In FIG. 6, the dispersion of positional displacementsshows a normal distribution curve when a process parameter is madevariable. In the case of normal distribution, the average and the modeagree with each other. On the other hand, in FIG. 7, the dispersion ofpositional displacements is asymmetric when a process parameter is madevariable. In this case, the mode is used in place of the average todetermine if the mask pattern needs to be modified or not.

While positional displacements of a pattern are computed in thisembodiment, it is also possible to compute the mask error factor (MEF)in a similar manner. In this case, the parameters to be used forcomputing positional displacements are limited to those that relate tothe mask. If the positional displacements are found to be greater than apredetermined value as a result of computations, the specification ofthe mask needs to be modified.

Similarly, when exposure parameters such as the NA, the partialcoherence, the lighting profile, the wavelength of light for exposureand the resist parameter are changed, the changes are fed back to thelithography margin. When aligner parameters such as the aberration ofthe aligner and the transmission distribution of the lens are changed,the changes are fed back to the parameters of the aligner. When assistbar parameters are changed, the changes are fed back to the rules of theassist bar. In this way, when the feedback destinations need to belimited, it is possible to check the positional displacements byselecting the parameters that are to be made variable.

The manner of arranging evaluation points and the manner of generatingpatterns are not limited to those of this embodiment and may be definedin various different ways depending on the required level of accuracyand the limit of the processing time.

2nd Embodiment

In an experiment using this embodiment, each of the process parameterswas made to be variable within a predefined range for a pattern obtainedby carrying out an operation of optical proximity correction on a maskpattern, following the flow chart of FIG. 8 to check the positionaldisplacements between the pattern to be generated on a wafer and thedesired pattern on the wafer for parameter. Then, the dispersion and theaverage of all the positional displacements were determined. As aresult, while the average was found within the predetermined range ofthe specification, the dispersion was found to be out of thepredetermined range. Therefore, a recommended layout was output byfollowing the sequence as described below to produce a desired patternon a wafer.

FIG. 8 is a flow chart summarily illustrating the sequence of the secondembodiment of pattern verification method according to the invention.FIGS. 9A through 9E are illustrations of the second embodiment ofpattern verification method according to the invention.

Firstly, draft circuit pattern data that are necessary for securing thedevice characteristics when designing an LSI or the like are prepared.Data for a mask pattern that is an enlarged draft circuit pattern arealso prepared by taking the scale reduction ratio of the projectionoptical system of the aligner (Step ST51). FIG. 9A illustrates a desiredpattern 10 on a substrate.

Then, dividing points P_(cu) are defined to divide the mask pattern intoparts having a predetermined length as shown in FIG. 9B (Step ST52).

Then, as shown in FIG. 9C, correction points P_(co) are defined atpredetermined positions on the divided edges (Step ST53). Alternatively,dividing points P_(cu) and correction points P_(co) may be directlydefined on the edges of the mask pattern.

Thereafter, an operation of optical proximity correction is conducted onthe edge of the mask pattern that corresponds to each (of the dividedparts?) of the defined edges (Step ST54). In Step ST54, the correctionquantity is computed on each of the defined correction points and thecorresponding edge of the mask pattern is shifted by the computedcorrection quantity.

Then, as shown in FIG. 9D, n evaluation points P_(i) (i=1 through n) aredefined on the edges of the desired pattern 10 (Step ST55).

Process parameters that can give rise to positional displacements ofpattern edges are defined (Step ST21). The process parameters mayinclude the film thickness of the resist film, the numerical apertureNA, the dose and the parameters for exposure including the defocusingvalue as well as post-exposure parameters such as the PEB temperatureand the development time. Then, a variable range is defined for eachprocess parameter (Step ST22). In this embodiment, the variable range ofthe dose is defined in terms of under dose˜the best dose˜over dose. Thevariable range of the focus position is defined in terms of the bestfocus˜defocus. The process parameters other than the dose and the focusposition are made invariable from the defined values.

Then, the positional displacement is determined for each of all thedefined evaluation points (Step ST56 through ST59). The method fordetermining the positional displacement is identical with that of thefirst embodiment and hence will not be described any further here.

The average and the standard deviation of the positional displacementsof all the evaluation points P_(i) (i=1 through n) are computed (StepST60). Then, it is determined if the standard deviation of thepositional displacements is found to be within a predefined range or not(Step ST61).

If the standard deviation is found to be out of the predefined variablerange, the desired pattern has to be modified (Step ST62). The largestpositional displacement of the edges is extracted out of all thepositional displacements of the edges computed for the evaluation pointson the desired pattern that has been divided and then another pattern 12is generated with edges shifted from those of the desired pattern by thelargest positional displacements (FIG. 9E) and a pattern is generatedwith edges shifted in opposite directions by the amounts obtained bydividing the extracted largest positional displacements by the MEF (maskerror factor, or the ratio of the dimensional change relative to thevariance of the mask).

In other words, it is possible to form a desired pattern on a wafer bymodifying the draft layout according to the output layout or provide adesign guideline.

If the standard deviation of the positional displacements is found to bewithin the predefined range, it is determined if the average of thepositional displacements is found to be within the predefined range ornot (Step S63). If the average of the positional displacements is foundto be out of the predefined range, the corrected mask pattern needs tobe modified (Step ST64).

If a plurality of evaluation points are used on the desired pattern inStep ST55, the same X coordinate and the same Y coordinate can be sharedby more than one evaluation points because evaluation points arearranged linearly. Thus, it is only necessary to carry out thecomputation of inverse Fourier transformation that involves a heavycomputational load for acquiring an optical image only once for anevaluation point because the result of the computation can be referredto for all the remaining evaluation points. In other words, thecomputational load of this embodiment does not rise significantly if thenumber of evaluation points is increased to raise the level of accuracyof evaluation.

FIGS. 9A through 9E schematically illustrate edges shifted by means oflithography simulation, using the technique of this embodiment, relativeto a desired pattern. The evaluation points illustrated in the drawingsare generated at positions with respective coordinates that arespecified in advance and arranged at dividing points and separated fromthe respective corners by 100 μm.

FIG. 10 shows the results of an operation of generating patterns near anedge of a desired pattern by varying the process parameter within apredetermined range, using the technique of this embodiment. In FIG. 10,reference symbol 21 denotes the optical image obtained as a result of atransfer simulation conducted with a reference exposure level and underthe best focus condition and reference symbol 22 denotes the opticalimage obtained as a result of a transfer simulation conducted with anexposure level energetically higher than the reference exposure leveland under the defocus condition of 0.2 μm, whereas reference symbol 23denotes the optical image obtained as a result of a transfer simulationconducted with an exposure level energetically lower than the referenceexposure level and under the defocus condition of 0.2 μm. Additionally,in FIG. 10, reference symbol 24 denotes the pattern generated within thearea of the divided desired pattern at a position with the largestpositional displacement of edge among the positional displacementsincluding those of the result of the transfer simulation with anexposure level energetically higher than the reference exposure leveland under the defocus condition of 0.2 μm and those of the desiredpattern and reference symbol 25 denotes the pattern generated within thearea of the divided desired pattern at a position with the largestpositional displacement of edge among the positional displacementsincluding those of the result of the transfer simulation with anexposure level energetically lower than the reference exposure level andunder the defocus condition of 0.2 μm and those of the desired pattern.From the obtained results, it was found that the largest absolute valueand the sign can be obtained from the positional displacements of thedesired pattern and those of the optical images obtained by the transfersimulations for all divided desired patterns.

FIG. 11 shows the results of displaying the recommended pattern obtainedin Step ST62. In FIG. 11, reference symbol 33 (solid lines) denotes thelayout illustrating a desired pattern on a wafer and reference symbol 32(broken lines) denotes the layout illustrating the extent of the largesterror, whereas reference symbol 31 (dotted chain line) denotes therecommended layout for forming a desired pattern on a wafer. In anexperiment, it was possible to form a desired pattern on a wafer bydrawing a layout of shifting the edges according to the obtainedresults.

As a result of another experiment using a conventional technique and thetechnique of this embodiment and common data for the same process, itwas found that the conventional technique consumed 420 hours, whereasthe technique of this embodiment consumed only 61 hours.

In this embodiment, three combinations including (the best dose/the bestfocus), (over dose/defocus) and (under dose/defocus) are used to computethe positional displacement of the edges. However, it is possible tocompute for all possible combinations of doses and focusessimultaneously without any additional load. At the same time, it is alsopossible to compute the positional displacements that can be producedjust like the defined dose, the defined focus, the process parameters,the numerical aperture of the aligner, the coherence factor, the centershielding ratio and/or the aberration change. Additionally, it is alsopossible to modify the mask pattern or redo the operation of proximitycorrection by comparing the dispersion and the average of the computedpositional displacements. Furthermore, it is possible to use all or partof the parameters of the items that can participate in positionaldisplacement and hence the parameters that are used in this embodimentare not limited to those listed above.

FIG. 12 shows a method of displaying a marker that indicates thepositional displacement when a single process parameter is used. FIG. 13shows a method of displaying markers that respectively indicate thepositional displacements when more than one process parameters are used.When a single process parameter is used, markers 41 are displayed atrespective evaluation points to indicate so many positionaldisplacements between the pattern obtained as a result of a transfersimulation and the mask pattern as shown in FIG. 12. When, on the otherhand, more than one process parameters are used, different markers 43are displayed and the dispersion and the average of all the markers arecomputed as shown in FIG. 13. In FIG. 13, Ed denotes the position of anedge of the desired pattern and Eavg denotes the average position of thepositional displacements of the edge.

While this embodiment is described for conducting an operation ofoptical proximity correction with the ordinary correction method, theuse of optical proximity correction is not limited to the ordinarycorrection method and the verification method of this embodiment can beused for proximity correction by taking the lithography margin intoconsideration. Then, the technique of narrowing down the correction isdifferent from the technique that is used with the conventional method,as shown in FIG. 14.

More specifically, an operation of proximity correction is conductedwhen the average of positional displacements and the displacement of adesired pattern are large. With the conventional method, the correctionis narrowed down so as to make the results of a simulation and thedesired edge positions agree with each other under optimal conditions ofthe device. On the other hand, when an operation of proximity correctionis conducted with this embodiment by taking the lithography margin intoconsideration, the correction is narrowed down so as to make the averageedge positions EP_(AVG) obtained as a result of a simulation and thedesired edge positions EP_(D) agree with each other.

Additionally, the verification method of this embodiment can be appliedto a new desired pattern obtained by adding the transformationdifference to a desired pattern. While the narrowed down position isthat of the desired pattern under optimal conditions of the device withthe conventional method, the narrowed down position is shifted to theedge position EP_(D2) obtained by adding the transformation difference(FIG. 15) when a transformation difference is added thereto. However,the evaluation point may remain on the original desired edge positionEP_(D1) (before the transformation difference is added).

While positional displacements of a pattern are computed in thisembodiment, it is also possible to compute the mask error factor (MEF)in a similar manner. In this case, the parameters to be used forcomputing positional displacements are limited to those that relate tothe mask. If the positional displacements are found to be greater than apredetermined value as a result of computations, the specification ofthe mask needs to be modified. Similarly, when exposure parameters suchas the numerical aperture NA, the partial coherence, the lightingprofile, the wavelength of light for exposure and the resist parameterare changed, the changes are fed back to the lithography margin. Whenaligner parameters such as the aberration of the aligner and thetransmission distribution of the lens are changed, the changes are fedback to the parameters of the aligner. When assist bar parameters arechanged, the changes are fed back to the rules of the assist bar. Inthis way, when the feedback destinations need to be limited, it ispossible to check the positional displacements by selecting theparameters that are to be made variable.

The manner of arranging evaluation points and the manner of generatingpatterns are not limited to those of this embodiment and may be definedin various different ways depending on the required level of accuracyand the limit of the processing time.

3rd Embodiment

As patterns are micronized, the precision level of corners may need tobe raised particularly when computing the positional displacements ofedges by means of the first or second embodiment. A technique (a splinetechnique) of computing a positional displacement that is different fromStep ST14 of the first embodiment and Step ST57 of the second embodimentis used in this embodiment. This will be described below.

A reference light intensity is defined. A number of auxiliary evaluationpoints are automatically defined in a direction perpendicular to an edgefor the evaluation points defined on the edge. The automaticallygenerated auxiliary evaluation points are found within an area extendedfrom a point on the edge of the desired pattern by 30 nm to the oppositelateral sides. A total of 6 evaluation points are added at regularintervals of 10 nm. These evaluation points are selected as tradeoffwith the processing speed. In an experiment conducted for thisembodiment, the area for generating evaluation points and the intervalsof evaluation points were made to vary in order to find out conditionsthat make the difference between the edge position of an optical imageand that of the desired pattern at each evaluation point selected by theconventional method not exceeding 1 nm.

The light intensity of each of the evaluation points and that of each ofthe auxiliary evaluation points are determined. Then, the lightintensity at a point between any two adjacently located evaluationpoints is determined by interpolation and the positional coordinate t₂of the point whose light intensity is determined by interpolation so asto be used as reference light intensity is computed by means of thespline method. Then, t₂−t₁ is defined as positional displacement.

The above-described method of computing the positional displacement isapplied to the second embodiment to obtain a recommended pattern. Sincethe obtained recommended pattern is similar to the one obtained in theabove description of the second embodiment, it will not be describedhere. However, the difference between this embodiment and the secondembodiment is clear by comparing the positional displacements of all theevaluation points of this embodiment with those of the secondembodiment.

In an experiment, patterns same as the one evaluated by means of thefirst embodiment were evaluated by means of the spline method andcompared with the desired pattern for positional displacements. Thepatterns that were evaluated have a rectangular profile having a longside of 1 μm and a short side of 0.09 μm. Masks of two different types,one with a dark field and the other with a bright field, were prepared.FIGS. 16A and 16B schematically illustrate the patterns. FIG. 16A showsthe dark field mask and FIG. 16B shows the bright field mask. In FIGS.16A and 16B, reference symbol 51 denotes an aperture and referencesymbol 52 denotes a shield.

An operation of optical proximity correction was conducted on thesemasks. The exposure conditions included the dose wavelength: 193 nm, thenumerical aperture (NA): 0.75, the coherence factor (σ): 0.85, the useof ⅔ annular illumination (shielding ratio of center of illumination)and reference dose I_(th)=0.218. Then, the positional displacementsbetween the edges of the pattern formed on a wafer by using the masksafter the correction, taking a development model into consideration, andthose of the desired pattern were computed.

FIG. 16A shows the pattern obtained by using the dark field mask (theinside of the edges is an aperture and the surrounding of the edges is ashield) and FIG. 16B shows the pattern obtained by using the brightfield mask (the inside of the edges is a shield and the surrounding ofthe edges if an aperture).

FIG. 17 is a graph illustrating the positional displacements under thebest focus/best dose conditions. In FIG. 17, the solid line, the brokenline and the dotted line respectively indicate the positionaldisplacements determined by the spline method, the slope method and theconventional method (light intensity is calculated by Hopkins'sequation). From FIG. 17, it will be seen that the positionaldisplacements determined by the spline method substantially agree withthose determined by the conventional method including the corners (theopposite ends of the X-axis).

FIG. 18 is a graph illustrating the differences (broken line) betweenthe conventional method and the slope method and the differences (solidline) between the spline method and the conventional method under thebest focus/best dose conditions. It will be seen from FIG. 18 that thedifferences between the spline method and the conventional method aresmall.

FIG. 19 is a graph illustrating the positional displacements under thedefocus/best dose conditions. In FIG. 19, the solid line, the brokenline and the dotted line respectively indicate the positionaldisplacements determined by the spline method, the slope method and theconventional method. FIG. 20 is a graph illustrating the differences(broken line) between the conventional method and the slope method andthe differences (solid line) between the spline method and theconventional method under the defocus/best dose conditions. It will beseen from FIG. 20 that the differences between the spline method and theconventional method are small. Even under the defocused condition thedifferences between the spline method and the conventional method aresmall.

FIGS. 21 through 24 illustrates the results obtained by changing themask pattern to a bright pattern. In these graphs, it will be seen thatthe results obtained by the spline method show smaller differences thanthose obtained by the conventional method.

FIG. 21 is a graph illustrating the positional displacements under thebest focus/best dose conditions. FIG. 22 is a graph illustrating thedifferences between the conventional method and the slope method and thedifferences between the spline method and the conventional method underthe best focus/best dose conditions. FIG. 23 is a graph illustrating thepositional displacements under the defocus/best dose conditions. FIG. 24is a graph illustrating the differences between the conventional methodand the slope method and the differences between the spline method andthe conventional method under the defocus/best dose conditions.

In FIGS. 21 and 23, the solid line, the broken line and the dotted linerespectively indicate the positional displacements determined by thespline method, the slope method and the conventional method. In FIGS. 22and 24, the broken line indicates the differences between theconventional method and the slope method and the solid line indicatesthe differences between the spline method and the conventional method.

In this embodiment, three combinations including (the best dose/the bestfocus), (over dose/defocus) and (under dose/defocus) are used to computethe positional displacement of the edges. However, it is possible tocompute for all possible combinations of doses and focusessimultaneously without any additional load. At the same time, it is alsopossible to compute the positional displacements that can be producedjust like the defined dose, the defined focus, the process parameters,the numerical aperture of the aligner, the coherence factor, the centershielding ratio and/or the aberration change. Additionally, it is alsopossible to modify the mask pattern or redo the operation of correctionby comparing the dispersion and the average of the computed positionaldisplacements. Furthermore, it is possible to use all or part of theparameters of the items that can participate in positional displacementand hence the parameters that are used in this embodiment are notlimited to those listed above.

4th Embodiment

This embodiment provides a technique of determining the light intensity(log dose) on a desired pattern edge on a wafer and the slope of thelight intensity within the range of a predetermined focus margin for alayout and verifying the pattern by using the processing sequence asillustrated in the flow chart of FIG. 25.

FIG. 25 is a flow chart summarily illustrating the sequence of thefourth embodiment of pattern verification method according to theinvention. In FIG. 25, the steps same as those of the flow chart of FIG.1 are denoted respectively by the same reference symbols and will not bedescribed any further. This embodiment will be described also byreferring to the ED-tree of FIG. 26.

In an experiment using this embodiment, a layout of a 90 nm line andspace (LS) pattern was used. The light intensity after the exposure anddevelopment process was computed under the predetermined conditionsincluding of the dose wavelength: 193 nm, NA: 0.75, σ: 0.85 and ε: 0.67.

The size tolerance and the focus margin (defocus value) are defined(Step ST82). In the case of this embodiment, the defocus value is 0.15μm when a size tolerance of 0.01 μm is given.

The light intensity and the slope of the function expressing the lightintensity are computed under the two conditions of the best focuscondition and the defocus condition (Step ST74), in a manner asdescribed below.

As in the case of the first embodiment, the light intensity I(t₁) at theevaluation point P_(i) with the positional coordinate t₁ on the desiredpattern 1 is computed by using the Hopkins formula (formula (1)).

$\begin{matrix}{{I(t)} = {\int{\int_{- \infty}^{\infty}{{{TCC}\left( {\omega,\omega^{\prime}} \right)} \times {M(\omega)} \times {{M\left( \omega^{\prime} \right)}\ }^{*} \times \exp \left\{ {{\left( {\omega - \omega^{\prime}} \right)}t} \right\} {\omega}{\omega^{\prime}}}}}} & (1)\end{matrix}$

Then, the differential quotient I′(t₁) of the first derivative (slope)of the light intensity I(t₁) at the evaluation point 11 with thecoordinate t₁ is computed by using formula (2) below.

$\begin{matrix}{{I^{\prime}(t)} = {\int{\int_{- \infty}^{\infty}{{{TCC}\left( {\omega,\omega^{\prime}} \right)} \times {M(\omega)} \times {{M\left( \omega^{\prime} \right)}\ }^{*} \times {\left( {\omega - \omega^{\prime}} \right)} \times \exp \left\{ {{\left( {\omega - \omega^{\prime}} \right)}t} \right\} {\omega}{\omega^{\prime}}}}}} & (2)\end{matrix}$

The values obtained on the desired pattern edge include the lightintensity (log dose): 0.2182069 and the slope: 1.819103 under the bestfocus condition and the light intensity (log dose): 0.217902 and theslope: 1.605271 under the defocus condition (0.15 μm defocus). Thedifference of exposure between the best focus condition and the defocuscondition is 0.0003049.

On the other hand, when the size tolerance and the slope are given, thedose margin that is allowed when forming an edge within the sizetolerance is given by the formula of

dose margin=light intensity(logdose)[non-dimensional]+slope[1/μm]×size[μm].

Thus, the dose margin is computed by using the slope and the sizetolerance determined under the best focus condition and those determinedunder the defocus condition.

As for the best focus, the dose margin DM_(b) is 0.0182 when an slope of1.819103 and a size tolerance of 0.01 μm are given.

A value of 8.56% is obtained by transformation into the ratio relativeto the reference light intensity I_(th) (threshold value for formingedges of a pattern) of 0.201089 as given in the first embodiment.

As for the defocus, the dose margin DM_(d) is 0.0161 when an slope of1.605271 and a size tolerance of 0.01 nm are given. A value of 7.98% isobtained as ratio relative to the reference light intensity.

From these values, the single dose margin DM_(s) of this layout isdetermined. A single dose margin DM_(s) is defined by the formula below.

single dose margin={smaller of dose margin DM_(b) and dose marginDM_(d)}−(value obtained by reducing the difference D between lightintensity for best focus and light intensity for defocus to dose margin)

From the above formula, the single dose margin DMS is computed to obtain7.97% from 7.89%−0.01452% (by reducingdifference=1.819103−1.605271=0.000305 to dose margin, using referencelight intensity 0.201089) (Step ST77). The dose margin of this layout asdetermined by the conventional method is 7.75%. Therefore, the twovalues substantially agree with each other.

The dose margin that is allowed to the layout as determined in Step ST76is 7%. It is possible to judge if the necessary margin is provided forthe layout at a desired edge or not by comparing the dose margin(allowable margin) and the dose margin determined by this embodiment(computed margin) (Step ST77). In the case of a 90 nm LS pattern, it isjudged that the necessary margin is provided and the processingoperation proceeds to process the next evaluation point (Step ST79, StepST80).

The same processing operation was carried out for an 85 nm LS pattern.The obtained values include the light intensity: 0.2182099 and theslope: 1.450778 under the best focus condition and the light intensity:0.2178164 and the slope: 1.3636 under the defocus condition. The dosemargin determined on the basis of these results as in the case of 90LSwas 6.63% and it was judged that the value of 7% of the specificationhad not been achieved and hence the layout had to be modified.Information on the necessary modification of the layout is then output(Step ST78).

FIG. 27 is a graph illustrating the results of an operation ofdetermining the margin of the same layout by means of the conventionalmethod and also by means of the method of this embodiment. It will beseen that they agree with each other to a considerably extent.

When determining the margin by the conventional method, the sizes atthree points including the evaluation point and the two size tolerancepoints are computed under the best focus condition and also under thedefocus condition. Therefore, a total of six computations are requiredfor the light intensity. To the contrary, with the method of thisembodiment, it is only necessary to compute the light intensity and theslope at two points including the evaluation point under the best focuscondition and the evaluation point under the defocus condition.

In the formulas (1) and (2), the part of exp(i(ω−ω′)t) requires a largecomputational load. However, in the case of this embodiment, it ispossible to refer to the result of computation obtained at the time ofdetermining the light intensity at the reference point when determiningthe slope by using the formula (2) and hence it is not necessary tocompute that part once again. The ratio of the time necessary for simplyreferring to the result of computation of exp(i(ω−ω′)t) to the timenecessary for computing exp(i(ω−ω′)t) is 1:10. Therefore, the ratio ofthe time necessary for the computations of the six items to the timenecessary for computing the two items and their respective slopes is6:2.2. In other words, the computing time is reduced to about ⅓. Thus,as a result, it is possible to improve the TAT of the verification.

5th Embodiment

In an experiment using this embodiment, the dose margin was determinedby carrying out computations same as those of 1st Embodiment for a 90 nmisolated (ISO) pattern. The obtained values include the light intensity:0.2164658 and the slope: 3.321888 under the best focus condition and thelight intensity: 0.2005 and the slope: 3.142987 under the defocuscondition. The single dose margin determined on the basis of theseresults was 7.6%. The dose margin required for this layout is 7% andhence it was judged that the necessary margin is provided and theprocessing operation proceeded to the next step.

In another experiment, the obtained values include the light intensity:0.2184965 and the slope: 3.307209 under the best focus condition and thelight intensity: 0.241642 and the slope: 3.132345 under the defocuscondition. The margin determined on the basis of these results was 4.06%and it was judged that the value of the specification had not beenachieved and hence the layout had to be modified. Information on thenecessary modification of the layout is then output.

The operation of verifying the layout, for which a single dose margin isprovided, can be made to proceed by combining the result of determiningthe single dose margin of the fourth embodiment and that of the fifthembodiment. More specifically, both the 90LS pattern and the 90ISOpattern are provided with a single dose margin. The value of the singledose margin of 90LS, that of 90ISO and the difference of the exposuresunder the best focus condition may be used for discussing a commonmargin for them.

The difference of the exposures under the best focus conditioncorresponds to a margin of (0.2184658−0.2182069/0.201989=0.12%. Thecommon margin is 7.6+0.12=7.72% and hence satisfies the requirement ofthe specification, which is 7%. If it is smaller than 7%, information onthe necessary OPC modification is output.

A typical layout for products is used to determine the margin and verifythe pattern by the fourth and the fifth embodiments. However, thepresent invention is by no means limited to specific patterns describedabove for the preferred embodiments and the present invention can beused to verify various layouts. The dose conditions are not limited tothose described above for the preferred embodiments and may be definedappropriately according to the target layout.

When the margin is provided by the specification, the layout can beverified by seeing if the slope of each evaluation point is found withinthe allowable limits of slope or not by using

minimal value of slope=Δlight intensity/ΔCD and Δlight intensity=thechange in the dose within the expected dose margin.

6th Embodiment

The fourth and fifth embodiments are effective when a mask that issubjected to proximity correction is used for a pattern. When the lightintensity (I) of the pattern and the reference light intensity (I_(th))of the device are relatively close to each other, it is possible toapproximate the slope at the position of the reference light intensityI_(th) by using the slope of the light intensity at the evaluationpoint. However, if they are not close to each other, the slope of lightintensity is not necessarily continuous and the approximation mayinvolve an error. If such is the case, the exposure margin can bedetermined by computing the difference between the light intensity atthe auxiliary point obtained by moving the reference point by the sizetolerance and the light intensity at the reference point and determiningthe ratio of the difference to the reference light intensity.

In this embodiment, the exposure margin determined by theabove-described method is used as index for judgment on the pattern. Inan experiment, this technique was applied to the 85 nm L/S patterndescribed above by referring to the fourth embodiment. Firstly, as forthe best focus margin, the light intensity at the evaluation point was0.218099 and the light intensity at the auxiliary point (evaluationpoint+4.25 nm) was 0.204726. By using the difference of these values andthe reference light intensity of the device, or 0.201089, the best focusmargin was determined to be (0.218099−0.211412)/0.201089×100=3.325%.Since this value is equal to the value that is obtained by moving by ahalf of the size tolerance, the value obtained by moving in oppositedirections is 3.325×2=6.65%.

Similarly, as for the defocus margin, the light intensity at theevaluation point was 0.2178164 and the light intensity at the auxiliarypoint was 0.21116. The margin determined as in the case of the bestfocus margin was 6.62%. The single dose margin as obtained bydetermining the ratio of the difference of the light intensity for thebest focus and the light intensity for the defocus to the referencelight intensity, or 0.14%, was 6.48%. Thus, it was judged that the valueof 7% of the specification had not been achieved and hence the layouthad to be modified. Information on the necessary modification of thelayout is then output.

7th Embodiment

FIG. 28 is a flow chart summarily illustrating the sequence of theseventh embodiment of pattern verification method according to theinvention.

Firstly, a desired pattern 61 (FIG. 29A) and a mask pattern 62 (FIG.29B) that has been subjected to proximity correction in order to formthe desired pattern on a substrate are prepared (Step ST91). The maskpattern has been subjected to optical proximity correction and/orprocess proximity correction.

Conditions (first conditions) are defined for the integrated circuitpattern data (Step ST92). A simulation is conducted under the firstconditions to determine the profile of the first pattern to be formed ona processing substrate (Step ST93). FIG. 30A illustrates the pattern 71obtained by the simulation. It is assumed that an aligner withilluminating condition ArF is used for the integrated circuit and thepattern is transferred under the conditions of NA=0.75, σ=0.85 and ε=⅔and in this embodiment.

Then, the profile of the desired pattern on the processing substrate andthe profile of the pattern formed on the processing substrate asdetermined by the above described simulation are compared and the spotsshowing a large difference are extracted (Step ST94). A large differencemay be defined as 10% of the smallest line width and the space permittedby the design rules or 10% of the design size of the selected spot. Thissequence is identical with the sequence of the conventional simulationfor extracting spots showing a large difference between the profile ofthe desired pattern and the profile of the pattern obtained bysimulation. In FIG. 30A, reference symbol 72 denotes a polygon thatindicates a spot where the difference is large. Such a spot is output inthe form of a polygon that is an error mark contained in the integratedcircuit pattern data.

Then, the second conditions that are different from the first conditionsincluding NA=0.75, σ=0.85 and ε=⅔ ann, defocus value=0.1 μm and +5% doseare defined for the same integrated circuit pattern data (Step ST95). Asimulation is conducted under the second conditions to determine theprofile to be produced on the processing substrate (Step ST96). FIG. 30Billustrates the pattern 72 obtained by the simulation.

While the first conditions and the second conditions differ in terms offocus and dose in this instance, factors that can produce differences ofconditions may include 1) focus, 2) dose, 3) aberration, 4) illuminationprofile, 5) illumination conditions and 6) resist type.

Then, as in the case of the first conditions, the profile of the desiredpattern 61 on the processing substrate and the profile of the pattern 72formed on the processing substrate as determined by the above describedsimulation are compared and the spots showing a large difference areextracted (Step ST97). In FIG. 30B, the spots 82 and 83 showing a largedifference are indicated by respective polygons 82.

Then, the spot extracted solely under the first conditions, the spot 83extracted solely under the second conditions and the spots 81, 82extracted under the first and second conditions are sorted by comparingthe spots extracted under the first conditions and those extracted underthe second conditions (Step ST98).

For instance, the first conditions include NA=0.75, σ=0.85 and ε=⅔ ann,defocus value=0 μm and the second conditions include NA=0.75, σ=0.85 andε=⅔ ann, defocus value=0.1 μm and +5% dose, the spot extracted undersolely under the first conditions and the spots extracted under thefirst and second conditions indicate that the “optical proximitycorrection per se” or the “integrated circuit pattern data per se” isproblematic. The spot extracted solely under the second conditionsindicate that the “optical proximity correction” per se is notproblematic and the dose margin itself is small so that some measureshave to be taken.

As described above, it is possible to tell whether the differencebetween the pattern profile and the desired pattern profile isattributable to the desired pattern or to the process conditions bydetermining the pattern profile formed on the substrate by means of amask pattern under a plurality of process conditions, extracting spotsshowing a large difference between the determined pattern profile andthe desired profile and sorting the extracted spots according to thepattern conditions.

No new computer program has to be developed for the comparison. For thepurpose of the present invention, it is possible to use a commerciallyavailable tool (DRC) for confirming the design rules including onedefining the width of the layout. While it is possible to acquirepattern XOR output in the form of a polygon, the format of polygon canvary “slightly” from tool to tool so that it may be necessary to conductan ambiguous retrieval operation. While ambiguity may be defined invarious different ways, it may for example be so defined that the totalsum of the differences of the sides of polygons is not greater than themaximum correction unit that is selected at the time of OPC if “thenumber of corners is same” and “the length of each side of the polygons”is small.

8th Embodiment

Now, the eighth embodiment of the present invention, which includes apattern verification computer program and a pattern verification system,will be described below by referring to FIG. 28.

Referring to FIG. 31, the pattern verification system 100 comprises acomputer 101 that performs arithmetic operations and controls variouscomponents of the system, a memory section 102 for storing the outcomeof arithmetic operations, a verification computer program and so on, aninput section 103 to be used for inputting various input data, a storagemedium input/output section 104 to be used for writing the verificationcomputer program from the storage medium such as optical disk thatstores the verification comparator program prepared by some othercomputer, draft circuit pattern and data for a mask pattern into thememory section 102 and a display section 105 for displaying theinput/output information and the outcome of arithmetic operations. Averification computer program for executing any of the above-describedfirst through sixth embodiments of pattern verification method isinstalled in the edge positional displacement verification system 100.

The verification program is input to the storage section 102 typicallyby the user watching the display section 105 and operating the inputsection 103, which may be a keyboard. If the verification computerprogram is prepared by some other computer, it may be input to thecomputer 101 and stored in the storage section 102 by way of a storagemedium such as optical disk and the storage medium input/output section104.

The verification computer program can be executed as the user retrievesit from the storage section 102 storing it to an operating section ofthe computer and inputs necessary data including data for initializationby way of the input section 103. As the arithmetic operations arecompleted, the obtained data on the positional displacements of theedges and the data necessary for modifying the design data are stored inthe storage section 102 so that they may be displayed on the displaysection 105 and/or output to the printer (not shown) and/or to any ofvarious storage mediums including disks of different types andsemiconductor memories whenever necessary, from the storage mediuminput-output section 104.

While a stand-along verification system is described above, a patternverification system according to the invention may be provided with acommunication adaptor (not shown) or the like for connecting the systemto a data processing network.

Mask can be manufactured by using a mask pattern verified by any of thepattern verification methods described in above embodiments or arecommended pattern obtained as a result of verification. It is alsopossible to conduct a lithography process for manufacturingsemiconductor devices by using a manufactured mask.

Additional advantages and modifications will readily occur to thoseskilled in the art. Therefore, the invention in its broader aspects isnot limited to the specific details and representative embodiments shownand described herein. Accordingly, various modifications may be madewithout departing from the spirit or scope of the general inventiveconcept as defined by the appended claims and their equivalents.

1-14. (canceled)
 15. A pattern verification method comprising: preparinga desired pattern and a mask pattern to form a first transferred/formedpattern corresponding to the desired pattern on a substrate; generatingedges by dividing the edge of the mask pattern by a predeterminedlength; defining a correction point on each of the edges generated bydividing the edge of the desired pattern; computing a correctionquantity in consideration of the proximity effect for each of thecorrection points; forming a correction mask pattern by moving thegenerated edges according to the computed correction quantities;defining at least one evaluation point on the edge of the correctionmask pattern; defining at least one process parameter to form a secondtransferred/formed pattern which being resist pattern formed on thesubstrate by using the correction mask pattern or being secondtransferred/formed pattern formed on the substrate by using the resistpatterns as a mask; defining a reference value and a variable range foreach of the process parameters to form the second transferred/formedpattern; computing a positional displacement for each first points onthe second transferred/formed pattern corresponding to the evaluationpoint, the first points computed using correction mask pattern and aplurality of combinations of parameter values obtained by varying theprocess parameters within the variable range or within the respectivevariable ranges, the positional displacement being displacement betweenfirst point and the evaluation point; computing a statistic of thepositional displacements for the evaluation points; and outputtinginformation to modify the mask pattern according to the statistic. 16.The method according to claim 15, wherein the information is amounts ofshifts of the edge as determined at the evaluation points.
 17. Themethod according to claim 16, wherein leading out the informationincludes extracting the maximum value out of the positionaldisplacements computed for the evaluation points; and determining theamount of shift of the edge of the desired pattern corresponding to themaximum value.
 18. The method according to claim 17, wherein theinformation is a quantity obtained by dividing the maximum positionaldisplacement by a constant.
 19. The method according to claim 18,wherein the constant is a mask error factor.
 20. The method according toclaim 15, wherein the statistic is a value of the standard deviation ofthe positional displacements, the average of the positionaldisplacements, and the mode of the positional displacements.
 21. Themethod according to claim 20, further comprising: comparing the standarddeviation of the positional displacements and a first predefined range;changing the desired pattern provided in a case where the standarddeviation of the positional displacement is out of the first predefinedrange; comparing the average of the positional displacements and asecond predefined range provided in a case where the standard deviationof the positional displacements is within the first predefined range;and outputting information to modify the correction mask patternprovided in a case where the average of the positional displacements isout of the second predefined range.
 22. The method according to claim20, wherein the process parameters provide an asymmetric distribution ofpositional displacements relative to the desired pattern, the methodfurther comprises: comparing the standard deviation of the positionaldisplacements and a third predefined range; outputting information tomodify the desired pattern provided in a case where the standarddeviation of the positional displacements is out of the third predefinedrange; or comparing the mode of the positional displacements and afourth predefined range provided in a case where the standard deviationof the positional displacements is within the third predefined range;and outputting information to modify the correction mask patternprovided in a case where the mode of the positional displacements isgreater than the fourth predefined range. 23-36. (canceled)
 37. Apattern verification system comprising: storing section configure tostore a desired pattern and a mask pattern to form the desired patternon a substrate; dividing section configure to generate a group of edgesby dividing each edge of the mask pattern by a predetermined length;correction point defining section configure to define a correction pointon each of the edges generated by dividing each edge of the desiredpattern; correction quantity computing section configure to compute acorrection quantity, taking the proximity effect into consideration, foreach of the correction points; forming section configure to form acorrection mask pattern by deforming the mask pattern according to thecomputed correction quantity; evaluation point defining sectionconfigure to define at least one evaluation point on each edge of thedesired pattern; process parameter defining section configure to defineat least one process parameter to compute the transferred/formedpattern; reference value defining section configure to define areference value and a variable range for each of the process parameters;positional displacement computing section configure to compute apositional displacement for each first points corresponding to theevaluation point, first points computed using correction mask patternand a plurality of combinations of parameter values obtained by varyingthe process parameters within the variable range or within therespective variable ranges, the positional displacement beingdisplacement between first point and the evaluation point; statisticcomputing section configure to compute a statistic of the positionaldisplacements computed for the evaluation point or for the evaluationpoints; and outputting section configure to output information to modifythe mask pattern according to the statistic.
 38. (canceled)